My head is literally on a swivel, and there's so much anatomy holding the spine together and surrounding it to make the idea of just popping a head off absurd.

One of the primary ligaments that holds the vertebrae together from the base of the skull to the pelvis is the anterial longitudinal ligament, and its mean breaking load is described as 600 Newtons. Tensile strength of the ligamentum flavum is 300 N, and the third end-to-end spinal ligament is the posterior longitudinal ligament, coming in at a relatively puny 67-138 N. (From: Sanford J. Larson & Dennis J. Maiman (1999) Surgery of the Lumbar Spine

And that's not counting the resistance offered by the muscles such as the scalenes and trapezius, and the skin.